I came across the following question in my NMR course for chemists:

Assuming that magnetization along the y-axis gives rise to an absorption mode
lineshape, draw sketches of the spectra which arise from the following operators:
$I_{1y}$ ; $I_{2x}$ ; $2I_{1y}I_{2z}$ ; $2I_{1z}I_{2x}$
Describe each spectrum in words.

This is the solution I was provided with:

enter image description here

My questions: Why are the signals split? Why are there two offsets? How can I derive the line shape?

I understand how the shape of the signal - absorption or dispersion - is influenced by the phase of the magnetisation vector. I read the chapter 8.4 about signal phases in the textbook “NMR spectroscopy” by Günther. However, I am still quite unsure how to approach this question, so I would appreciate any explanation or advice. References of any kind are welcomed. As mentioned, I mostly use Günthers and Keelers textbooks for learning.



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